Topics: Derivative, Exponentiation, Real number Pages: 1 (297 words) Published: April 21, 2013
Unit 11 Mini-Analysis
Consider the following standard and semi-log plots from the Australian Bureau of Statistics. Both graphs show the probability (in decimal form) that an Australian woman of age x will die within the next year. | |

Remember to use complete sentences on each of the questions below, rounding to four decimal places where appropriate. Save the resulting document in either Word or PDF form and resubmit to the D2L dropbox. Your last name should appear in the name of the file. 1. The standard plot on the left appears exponential. However, by examining the semi-log plot on the right, we see that only a portion of the data is actually exponential. For what ages would you conclude that the probability (in decimal form) of dying in the next year is approximately exponential? Explain.

I do not understand the question. The ages that are approximately exponential are 22-90 on the right graph because these lines seem to form a straight line, similar to exponential growth.

2. Assuming that the points (44, -3) and (70, -2) are on the linear portion of the semi-log plot, create a linear function for Y=log⁡(y) as a function of x. Make sure to show your work.

-2+3/70-44 = 1/26 y=.0384615385x+b y = .0385x – 2.5

3. Rewrite your semi-log plot equation from #2 so that it now shows the exponential function that we can view on the standard plot. Make sure to show your work.

Y = .0385x + -2.5 y = 10^.0385x * 10^-2.5 1.0926^x * .0032

4. What percent does an Australian female’s probability of death (within the next year) increase every year?

The probability of women’s death in Australia increases by 9.26% each year.
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